By means of a 6-year panel of annual earnings data, we estimate the impact of a labour market training programme (LMT) targeted at unemployed adults. Unlike most nonexperimental studies, we use an internal comparison group of rejected applicants to measure the counterfactual outcome of trainees. For a subsample of applicants, rejections were randomised on a course-by-course basis. Following Heckman and Hotz [J. Am. Stat. Assoc. 84 (1989) 862] we test alternative estimators. All models report positive effects of being offered training, though the effects are not always significantly different from zero. The linear control estimator reports significantly positive effects of training. Analysing courses with ordinary assignment, the pre-training test indicates a positive selection bias. Turning to applicants for courses with random assignment, the linear control model is not rejected by the pre-training test. The fixed effect, random growth and modified random growth models are rejected by the model restriction test; this is the case for courses with ordinary assignment as well as random assignment. We illustrate the value of an internal comparison group in estimating the counterfactual outcome of participants, by comparing the post-training outcomes of rejected applicants and unemployed nonapplicants. Rejected applicants have significantly higher post-training earnings than eligible nonapplicants, which indicates that self-selection into the programme is influenced by unobservables. In general, the results clearly support the view that reliable studies of training effects should be based on internal comparison groups. Moreover, the assumptions motivating nonexperimental estimators should be explicitly tested. (C) 2002 Elsevier Science B.V. All rights reserved.